In a known motor-driven chain saw (Zenoah G 455 AVS), the brake device for bringing the saw chain to standstill when there is a kickback of the chain saw is mounted in the sprocket wheel cover. This affords the advantage that the brake device with its trigger configured as a hand guard can be preassembled as an assembly unit with the sprocket wheel cover. The hand guard has an L-shaped configuration and is pivotally journalled on the sprocket wheel cover with one of the two leg ends; whereas, the other leg extends transversely to the longitudinal axis of the chain saw forward of the upper handle. The hand guard can also move transversely to the pivot axis because of the necessary assembly play which occurs with the bearing of the hand guard on the sprocket wheel cover. This can lead to erroneous triggering of the brake device. In this context, it must also be considered that with a trigger force acting on the free end of the leg of the hand guard, this force not only effects a pivoting movement of the hand guard, but also leads to a twisting torque in the bearing because of the acting lever conditions. The bearing in the sprocket wheel cover is therefore correspondingly heavily loaded whereby, even after a short operating time, the bearing play increases which increases the danger of an erroneous triggering of the brake device or, in an extreme case this can lead to functional inoperability of the triggering mechanism.